Volume 25, 2019
|Number of page(s)||20|
|Published online||23 July 2019|
Existence for dislocation-free finite plasticity
Faculty of Mathematics, University of Vienna,
2 Istituto di Matematica Applicata e Tecnologie Informatiche E. Magenes, v. Ferrata 1, 27100 Pavia, Italy
* Corresponding author: firstname.lastname@example.org
Accepted: 13 February 2018
This note addresses finite plasticity under the constraint that plastic deformations are compatible. In this case, the total elastoplastic deformation of the medium is decomposed as y = ye ○ yp, where the plastic deformation yp is defined on the fixed reference configuration and the elastic deformation ye is a mapping from the varying intermediate configuration yp(Ω). Correspondingly, the energy of the medium features both Lagrangian (plastic, loads) and not Lagrangian contributions (elastic).
We present a variational formulation of the static elastoplastic problem in this setting and show that a solution is attained in a suitable class of admissible deformations. Possible extensions of the result, especially in the direction of quasistatic evolutions, are also discussed.
Mathematics Subject Classification: 35K90
Key words: Finite plasticity / static problem / existence / quasistatic evolution
© EDP Sciences, SMAI 2019
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